Solving Differential Equations with Mathematica's Solver

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The solution you found should have been:

DSolve[y'[x]==y[x]/x+2x+1, y[x], x]
{{y[x] → x C[1] + x (2 x + Log[x])}}

In general, provided it doesn't encounter a knotty integral, Mathematica can solve any first order linear differential equation.

Now it's time for you to tackle some problems without any help from me whatsoever. So! To the problems...

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